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Find all the roots of f(x) = x^4-2x^3+5x^2-8x+4

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candygurlll | Student, College Freshman | eNoter

Posted April 8, 2012 at 9:51 AM via web

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Find all the roots of f(x) = x^4-2x^3+5x^2-8x+4

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 8, 2012 at 5:16 PM (Answer #1)

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The roots of f(x) = x^4-2x^3+5x^2-8x+4 have to be determined.

x^4-2x^3+5x^2-8x+4 = 0

=> x^4 - x^3 - x^3 + x^2 + 4x^2 - 4x - 4x + 4 = 0

=> x^3(x - 1) - x^2(x - 1) + 4x(x - 1) - 4(x - 1) = 0

=> (x^3 -x^2 + 4x - 4)(x - 1) = 0

=> (x^2(x - 1) + 4(x - 1))(x - 1) = 0

=> (x^2 + 4)(x - 1)^2  = 0

x - 1 = 0

=> x = 1

x^2 + 4 = 0

=> x = 2i and x = -2i

The roots of f(x) = x^4 - 2x^3 + 5x^2 - 8x + 4 are 2i, -2i and 1.

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